Figure 2: Optical measurements of metallic Ta/CoFeB/MgO.

Experimentally measured Kerr angle (θ_K) and (normalized) differential Kerr angle (Δθ_K) for the magnetic field parallel (a,b) or perpendicular (c,d) to the current with current density of 4.6 × 10⁶ A cm⁻² and with θ_S=θ_K(H_a=0). The schematics in a,b show the direction of the magnetic field with respect to the current. The arrow balls in a schematically show the direction of the magnetic moment at various magnetic field. The θ_K and Δθ_K are proportional to m_z and Δm_z, respectively. The sharp edges in a,c indicate OOP switching of the magnetization due to a small OOP component of the external field. The asymmetric and symmetric line shapes in b,d reflect the symmetries of the anti-damping-like and field-like spin–orbit effective fields under magnetization reversal, respectively. The current-induced dynamics of magnetization m and relevant directions of SOFs are schematically demonstrated in b,d. For j ||H_a, the anti-damping field is quantified by fitting equation (4) to the experiment at large fields (solid red lines in b). For j⊥H_a, the field-like effective field is measured from the curvature of θ_K (solid red line in c) and the slope of Δθ_K (solid red line in d). Comparison of optical (red box) and transport (blue circle) measurements of anti-damping-like and field-like effective fields at various current densities for Ta/CoFeB/MgO is shown in e,f, respectively. In e,f, the solid red lines are linear fits to the optical probe, whereas the dashed blue lines are linear fits to the transport results. In e, the fits quantify the anti-damping-like coefficients λ_AL at (2.01±0.01) × 10⁻⁶ and (1.87±0.01) × 10⁻⁶ Oe A⁻¹ cm² for optical and transport probes, respectively. In f, the field-like coefficients λ_FL for the optical and transport probes are measured at (3.28±0.03) × 10⁻⁶ and (3.34±0.02) × 10⁻⁶ Oe A⁻¹ cm², respectively. The error bars in e,f are obtained by linear regression. The error bars in e are smaller than symbols. The consistency demonstrates the equivalency and relevance of the MO probe technique for investigating the SOTs in magnetic structures.